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Parabolic Equations in Reifenberg Domains
Journal article   Peer reviewed

Parabolic Equations in Reifenberg Domains

Sun-Sig Byun and Lihe Wang
Archive for rational mechanics and analysis, Vol.176(2), pp.271-301
05/2005
DOI: 10.1007/s00205-005-0357-6

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Abstract

Natural Sobolev-type estimates are proved for weak solutions of inhomogeneous parabolic equations in divergence form in a bounded cylinder Ω*=Ω×(0,T] which is δ-Reifenberg flat in the space direction. The principal coefficients of the operator are assumed to be in BMO space with their BMO semi-norms small enough.
Mechanics Fluids Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks Mathematical and Computational Physics Physics Electromagnetism, Optics and Lasers

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